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Perimeter of the triangle is defined as the sum of all the sides of a particular triangle. It is a closed geometric object which involves the measurement of the outer boundary of the object.
- Perimeter of triangle is the sum of the entire sides of a closed geometric object.
- A ruler is usually used to measure the sides of regular shapes.
- The string is used to measure the boundary of irregular shapes.
- The triangle involves three sides of the two-dimensional figure.
- Any polygon can easily be divided into a triangle.
- With the help of the perimeter of a triangle, the fencing length of a triangular plot can be calculated.
- The unit of measurement includes inches, yards or feet.
Read More: Edges, Faces, and Vertices
Key Terms: Perimeter of Triangle, Triangle, Isosceles Triangle, Equilateral Triangle, Scalene Triangle, Right Triangle, Acute-Angled Triangle, Obtuse Angled Triangle
Perimeter of Triangle
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Perimeter of triangle is the total of all three sides. The term perimeter is a group of two greek verses which are “peri” which means around and “metron” which means measure.
- The complete distance around the two-dimensional figure is defined as its perimeter.
- Subsequently, the perimeter gives the length of the boundary of a shape and is expressed in linear units.
- For any triangle, one of the subsequent three circumstances should be true.
a + b > c
b + c > a
c + a > b
The formula for the Perimeter of Triangle is specified as,
Perimeter of Triangle is denoted as a + b + c
- where the a, b, c are just the sides of the triangle.
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Types of Triangle based on Sides
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The perimeter of triangle based on sides of different triangles are as follows:
Isosceles Triangle
A traingle is said to be an isoceles triangle when two sides of the triangle are equivalent.
Perimeter of an Isosceles Triangle equals to 2a + c
Solved Example of Perimeter of Isosceles TriangleGiven below is the solved example of Perimeter of Isosceles Triangle Example: In a triangle ABC, two sides of the triangle a= 20 cm and Base c= 8 cm Ans. The perimeter of Isosceles triangle equals to 2a + c Perimeter = 2(20) +8 = 48 cm |
Equilateral Triangle
A triangle is said to be an equilateral triangle when all sides of the triangle are equal.
Perimeter of an Equilateral Triangle equals to 3a
where a is the length of every side of the triangle.
Solved Example of Perimeter of Equilateral TriangleGiven below is the solved example of Perimeter of Equilateral Triangle Example: In a triangle ABC, the sides of the triangle is equivalent to 2 cm. Ans. The perimeter of equilateral triangle equals to 3a Perimeter = 3 x 2 = 6 cm |
Scalene Triangle
A triangle is said to be a scalene triangle when all the sides of the traingle are unequal.
Perimeter of Scalene Triangle is s + l + m
where s, l and m are three sides of triangle
Solved Example of Perimeter of Scalene TriangleGiven below is the solved example of Perimeter of Scalene Triangle Example: In a triangle ABC, the sides of the triangle is equivalent to 15 cm, 34 cm, 32 cm. Ans. Perimeter of Scalene Triangle is s + l + m Hence, perimeter = 15 + 34 + 32cm = 81cm |
Read More: Similarities of Triangle
Types of Triangle based on Angles
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The perimeter of triangle based on angles of different triangles are as follows:
Acute Triangle
A triangle is said to acute triangle when each angle of triangle is less than 90°. The sum of all interior angles of acute triangle is 180 degrees.
Solved Example of Perimeter of Acute TriangleGiven below is the solved example of Perimeter of Acute Triangle Example: Find the perimeter of an acute triangle whose sides are 12 units, 1 units and 5 units. Ans. The sides of the triangle are given as, a = 12 units, b = 1 units and c = 5 units. Perimeter of an acute triangle = a + b + c. After substituting the values in the formula, we get, Perimeter of an acute triangle = a + b + c = 12 + 1 + 5 = 18. Therefore, the perimeter of the acute triangle = 18 units. |
Obtuse Triangle
A triangle is said to obtuse triangle when each angle of triangle is more than 90°. The longest side of an obtuse traingle is equivalent to the side opposite to the required angle.
Solved Example of Perimeter of Obtuse TriangleGiven below is the solved example of Perimeter of Obtuse Triangle Example: Can sides measuring 3 inches, 4 inches, and 7 inches form an obtuse triangle? Ans. The sides of an obtuse triangle should satisfy the condition that the sum of the squares of any two sides is lesser than the square of the third side. We know that a = 3 in b = 4 in c = 7 in Taking the squares of the sides, we get: a2 = 9, b2 = 16, and c2 = 49 We know that, a2 + b2 < c2 49 > (9 + 16) The given measures can form the sides of an obtuse triangle. Therefore, 3 inches, 4 inches, and 7 inches can be the sides of an obtuse triangle. |
Right Triangle
A triangle is said to right triangle when each angle of triangle is equal to 90°. Among every three sides, one is the longest and the other two are base and perpendicular depending on which side holds the taken angle.
Perimeter formula of Right-Angle Triangle = a + b + c
- Where a and b are two legs of right angle and c is the reverse side of the right angle, which is termed as the hypotenuse.
- If the lengths of the sides are not mentioned, then Pythagoras Theorem is used.
- The theorem states that the addition of the square of both sides of a right angle equals the square of the hypotenuse.
- The Pythagoras Theorem is a2 + b2 = c2 .
- The value of two sides is termed then the perimeter can be written in the way a and b follows as P = a + b + √(a² + b²).
- where both a and b are the two specified legs of the triangle.
Read More: Congruence of Triangles
How to calculate Perimeter of Triangle?
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The perimeter of a triangle can be calculated by following the steps mentioned below:
Step 1
The measurements of every side of a triangle and check that every side has a similar unit.
Step 2
Analyze the sum of every side.
Step 3
Provide the answer along with the unit.
Solved Example of Perimeter of TriangleGiven below is the solved example of Perimeter of Isosceles Triangle Example: In a triangle ABC, two sides of the triangle a= 30 cm and Base c= 18 cm Ans. The perimeter of Isosceles triangle equals to 2a + c Perimeter = 2(30) + 18 = 78 cm Example: Find the perimeter of an acute triangle whose sides are 12 units, 11 units and 25 units. Ans. The sides of the triangle are given as, a = 12 units, b = 11 units and c = 25 units. Perimeter of an acute triangle = a + b + c. After substituting the values in the formula, we get, Perimeter of an acute triangle = a + b + c = 12 + 11 + 25 = 48. Therefore, the perimeter of the acute triangle = 48 units. |
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Things to Remember
- The perimeter of the triangle is the sum of all three sides of a triangle.
- The formula for the perimeter of triangle is determined to be a + b + c
- The formula for the perimeter of an isosceles triangle is determined to be 2a + c
- The perimeter of an equilateral triangle is determined to be 3x
- The perimeter of the scalene triangle is determined to be s + l + m
- Perimeter of right triangle is determined to be a + b + √(a² + b²)
Read More: Formula Of Perimeter Shapes
Sample Questions
Ques: Look for the perimeter of an equilateral triangle when the side is 6 cm. (2 marks)
Ans: In an equilateral triangle, each side shall be equal.
Hence, a = 6
The perimeter of an equilateral triangle is equal to a + b + c equals to a + a + a leads to 3a
= 3 x a
= 3 x 6 = 18 cm
Ques: Find the perimeter of a right-angle triangle with two legs of 6 cm and 3 cm. (3 marks)
Ans: h being the hypotenuse,
Now, h2 = 62 + 32.
h2 = 36 + 9
h2 = 45
Now, h shall be equal to √45 which is equal to 6.71.
The Perimeter is equals to 6.71cm + 6cm + 3cm = 15.71cm
The perimeter of the right triangle equals 15.71cm.
Ques: Search the perimeter of an isosceles right-angled triangle having a hypotenuse of 50 cm. (2 marks)
Ans: The isosceles right-angled triangle, let a = b
According to Pythagoras Theorem
a2 + a2 = 502
2a2 = 2500 (dividing both side by 2)
a2 = 1250
The Perimeter is equals to 2 a + 50 which is 2 √1250 + 50 equals to 50 (√ 2 + 1) =120.7 cm
Ques: The perimeter of an isosceles triangle is 26 cm and the length of every congruent side is 8 cm. Calculate. (2 marks)
Ans: Perimeter = 8 + 8 + x
26 = 8 + 8 + x
26 = 16 + x
x = 26 -16 = 10 cm
Ques: The other side of a triangle is twice as long as the shortest side and the third side is 15 cm. Evaluate the missing sides of the perimeter is 57 cm. (4 marks)
Ans: Let a be each of the sides of the triangle
According to the question, the other side will be
b = 2a
c = 15 cm
Perimeter = a + b+ c
57 = a + 2a + 15
57 = 3a + 15
57- 15 = 3a
42 = 3a
a = 42/3
a =14
Hence, b= 2a which equals to 2 x 14 which is 28
a= 14 cm, b = 28 cm
Ques: The side length of an equilateral triangle is about 9 cm. Find the perimeter of an equilateral triangle. (2 marks)
Ans: The side length of the equilateral triangle is s=9 cm,
Perimeter is equal to 3s, where s is the length of three equal edges.
Substituting the value of s in the beyond formula mentioned,
The, Perimeter =3×9 =27 cm
Therefore, the perimeter of an equilateral triangle is 27.
Ques: Evaluate the perimeter of a right triangle QPR with sides being PQ of 4 inches, QR of 3 inches, and where side PR was not known. (4 marks)
Ans: Above mentioned, the PQ = 4 inches, QR = 3 inches, what is PR =?
To estimate the perimeter of the triangle, we must know every three sides.
Analyze the dimensions of the hypotenuse using the Pythagoras theorem.
PR² = PQ² + QR²
PR² = 4² + 3²
PR² = 16 + 9
Therefore, PR = √25
PR = 5 inches.
Nowadays, calculate the perimeter of the triangle.
The perimeter of triangle PQR is equal to the sum of the three sides
Which is 3 + 4 + 5 = 12
Hence, the perimeter is about 12 inches.
Ques: Look for the perimeter of an equilateral triangle when the side is 7 cm. (2 marks)
Ans: In an equilateral triangle, each side shall be equal.
Hence, a = 7
The perimeter of an equilateral triangle is equal to a + b + c equals to a + a + a leads to 3a
= 3 x a
= 3 x 7 = 21 cm
Ques: Find the perimeter of an acute triangle whose sides are 12 units, 1 units and 5 units. (3 marks)
Ans: The sides of the triangle are given as, a = 17 units, b = 1 units and c = 15 units.
Perimeter of an acute triangle = a + b + c.
After substituting the values in the formula, we get,
Perimeter of an acute triangle = a + b + c = 17 + 1 + 15 = 33.
Therefore, the perimeter of the acute triangle = 33 units.
Ques: The other side of a triangle is twice as long as the shortest side and the third side is 12 cm. Evaluate the missing sides of the perimeter is 50 cm. (4 marks)
Ans: Let a be each of the sides of the triangle
According to the question, the other side will be
b = 2a
c = 12 cm
Perimeter = a + b+ c
50 = a + 2a + 12
50 = 3a + 12
50- 12 = 3a
38 = 3a
a = 38/3
Hence, b= 2a which equals to 2 x 38/3 which is 76/3
a= 38/3 cm, b = 76/3 cm
Ques: Find the perimeter of △ABC having the following dimensions: AB = 7 inches, BC = 5 inches, AC = 10 inches. (3 marks)
Ans: Check if all three sides of the triangle are known.
AB = 7 inches, BC = 5 inches, AC = 10 inches
Use the appropriate formula and add the sides to get the required perimeter.
It is a scalene triangle, we use the formula, Perimeter of scalene triangle= a + b + c.
Write the perimeter along with its units.
Perimeter of triangle ABC = 7 + 5 + 10 = 22 inches.
Ques: In a triangle ABC, the sides of the triangle is equivalent to 25 cm, 40 cm, 30 cm. (2 marks)
Ans. Perimeter of Scalene Triangle is s + l + m
Hence, perimeter = 25 + 40 + 30 cm = 95 cm
Ques: The perimeter of an isosceles triangle is 50 cm and the length of every congruent side is 18 cm. Calculate. (2 marks)
Ans: Perimeter = 18 + 18 + x
50 = 18 + 18 + x
50 = 36 + x
x = 50 – 36 = 14 cm
Ques: The other side of a triangle is twice as long as the shortest side and the third side is 10 cm. Evaluate the missing sides of the perimeter is 40 cm. (4 marks)
Ans: Let a be each of the sides of the triangle
According to the question, the other side will be
b = 2a
c = 10 cm
Perimeter = a + b+ c
40 = a + 2a + 10
40 = 3a + 10
40- 10 = 3a
30 = 3a
a = 10
Hence, b= 2a which equals to 2 x 10 which is 20
a= 10 cm, b = 20 cm
Ques: Find the perimeter of △ABC having the following dimensions: AB = 12 inches, BC = 25 inches, AC = 30 inches. (3 marks)
Ans: Check if all three sides of the triangle are known.
AB = 12 inches, BC = 25 inches, AC = 30 inches
Use the appropriate formula and add the sides to get the required perimeter.
It is a scalene triangle, we use the formula, Perimeter of scalene triangle= a + b + c.
Write the perimeter along with its units.
Perimeter of triangle ABC = 12 + 25 + 30 = 67 inches.
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